Computer is laggy when editing with Multiresolution
The issue for the slowdown is due to how dense your model is. Generally it's a trade-off between quality and performance. in this instance you are using a multi-resolution modifier as well as a subdivision modifier. Both modifiers accomplish pretty similar tasks however in this case your subdivision modifier is subdividing an already subdivided surface adding significantly more vertices than what is needed in your model. This is why your are experiencing such a large amount of slowdown due to the amount of subdivisions that are in place.

I recommend picking either the the multi-resolution modifier or the subdivision modifier and sticking with that.